The present invention relates to a new and distinct cultivar of Cordyline australis and is hereinafter referred to by the cultivar name ‘Zumba’. The new Cordyline is the product of a planned breeding program conducted by the inventor in Kihikihi, Waikato, New Zealand. The objective of the breeding program is to create new Cordyline cultivars with attractive foliage colors. ‘Zumba’ originated from a crossing in 2006 of the female or seed parent Cordyline ‘Red Fountain’ (not patented) and the male or pollen parent Cordyline ‘Albertii’ (not patented). The resulting seeds were subsequently planted and grown. The cultivar ‘Zumba’ was selected by the inventor in the 2010 as a single plant within the progeny of the stated cross in Kihikihi, Waikato, New Zealand. Asexual reproduction of the new cultivar ‘Zumba’ first occurred by tissue culture in 2013 in Auckland, New Zealand. Since that time, under careful observation, the unique characteristics of the new cultivar have been uniform, stable and reproduced true to type in successive generations of asexual reproduction.